Learning to solve Class-Constrained Bin Packing Problems via Encoder-Decoder Model

Neural methods have shown significant merit in solving combinatorial optimization (CO) problems, including the Bin Packing Problem (BPP). However, most existing ML-based approaches focus on geometric BPP like 3DBPP, neglecting complex vector BPP. In this study, we introduce a vector BPP variant called Class-Constrained Bin Packing Problem (CCBPP), dealing with items of both classes and sizes, and the objective is to pack the items in the least amount of bins respecting the bin capacity and the number of different classes that it can hold. To enhance the efficiency and practicality of solving CCBPP, we propose a learning-based Encoder-Decoder Model. The Encoder employs a Graph Convolution Network (GCN) to generate a heat-map, representing probabilities of different items packing together. The Decoder decodes and fine-tunes the solution through Cluster Decode and Active Search methods, thereby producing high-quality solutions for CCBPP instances. Extensive experiments demonstrate that our proposed method consistently yields high-quality solutions for various kinds of CCBPP with a very small gap from the optimal. Moreover, our Encoder-Decoder Model also shows promising performance on one practical application of CCBPP, the *Manufacturing Order Consolidation Problem* (OCP).